Having a gun in gameplay does not qualify a game as a shooter. In this case you should have made GTAIV a shooter but you did not because it is a sand-box game and the game isn't entirely based on just gunplay.

Uncharted is an action/adventure. Metal Gear Solid 4 is a Stealth/Espionage. This is just like how Splinter Cell isn't just a "shooter".

Yes MGS4 can be played like a shooter, but the core focus on gameplay is not, that is why there are trophies for killing no enemies and not tripping any alarms.